A model of ballistic aggregation and fragmentation

A simple model of ballistic aggregation and fragmentation is proposed. The model is characterized by two energy thresholds, Eagg and Efrag, which demarcate different types of impacts: If the kinetic energy of the relative motion of a colliding pair is smaller than Eagg or larger than Efrag, particles respectively merge or break; otherwise they rebound. We assume that particles are formed from monomers which cannot split any further and that in a collision-induced fragmentation the larger particle splits into two fragments. We start from the Boltzmann equation for the mass-velocity distribution function and derive Smoluchowski-like equations for concentrations of particles of different mass. We analyze these equations analytically, solve them numerically and perform Monte Carlo simulations. When aggregation and fragmentation energy thresholds do not depend on the masses of the colliding particles, the model becomes analytically tractable. In this case we show the emergence of the two types of behavior: the regime of unlimited cluster growth arises when fragmentation is (relatively) weak and the relaxation towards a steady state occurs when fragmentation prevails. In a model with mass-dependent Eagg and Efrag the evolution with a cross-over from one of the regimes to another has been detected

Chains of Viscoelastic Spheres

Given a chain of viscoelastic spheres with fixed masses of the first and last particles. We raise the question: How to chose the masses of the other particles of the chain to assure maximal energy transfer? The results are compared with a chain of particles for which a constant coefficient of restitution is assumed. Our simple example shows that the assumption of viscoelastic particle properties has not only important consequences for very large systems (see [1]) but leads also to qualitative changes in small systems as compared with particles interacting via a constant restitution coefficient.Comment: 11 pages, 6 figure

Molar substitution and C2/C6 ratio of hydroxyethyl starch: influence on blood coagulation

Background. Development of hydroxyethyl starches (HES) with a low impact on blood coagulation but a long intravascular persistence is of clinical interest. A previous in vitro study showed that low substituted high molecular weight HES does not compromise blood coagulation more than medium molecular weight HES. In the present study we assessed the individual effects on blood coagulation of molar substitution and C2/C6 ratio of a high molecular weight HES. Methods. Blood was obtained from 30 healthy patients undergoing elective surgery and mixed with six high molecular weight (700 kDa) HES solutions differing in their molar substitution (0.42 and 0.51) and C2/C6 ratio (2.7, 7 and 14) to achieve 20, 40 and 60% dilution. Blood coagulation was assessed by Thrombelastograph® analysis (TEG) and plasma coagulation tests.Data were compared using a three-way analysis of variance model with repeated measures on the three factors. Results. Higher molar substitution compromised blood coagulation most (for all TEG parameters, P0.50). The higher molar substitution was associated with a lesser increase in PT (P=0.007) and a greater decrease in factor VIII (P=0.010). PTT, functional and antigenic von Willebrand factors were not significantly influenced by molar substitution (P for all >0.20). No significant differences between solutions with the same molar substitution but different C2/C6 ratios were found in plasma coagulation parameters (P for all >0.05). Conclusions. TEG analysis indicates that high molecular HES with a molar substitution of 0.42 and a C2/C6 ratio of 2.7 has the lowest effect on in vitro human blood coagulatio

Localized and Cellular Patterns in a Vibrated Granular Layer

We propose a phenomenological model for pattern formation in a vertically vibrated layer of granular material. This model exhibits a variety of stable cellular patterns including standing rolls and squares as well as localized objects (oscillons and worms), similar to recent experimental observations(Umbanhowar et al., 1996). The model is an amplitude equation for the parametrical instability coupled to the mass conservation law. The structure and dynamics of the solutions resemble closely the properties of localized and cellular patterns observed in the experiments.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Self-diffusion in granular gases

The coefficient of self-diffusion for a homogeneously cooling granular gas changes significantly if the impact-velocity dependence of the restitution coefficient $\epsilon$ is taken into account. For the case of a constant $\epsilon$ the particles spread logarithmically slow with time, whereas the velocity dependent coefficient yields a power law time-dependence. The impact of the difference in these time dependences on the properties of a freely cooling granular gas is discussed.Comment: 6 pages, no figure

Upregulation of the voltage-gated sodium channel beta2 subunit in neuropathic pain models: characterization of expression in injured and non-injured primary sensory neurons

The development of abnormal primary sensory neuron excitability and neuropathic pain symptoms after peripheral nerve injury is associated with altered expression of voltage-gated sodium channels (VGSCs) and a modification of sodium currents. To investigate whether the beta2 subunit of VGSCs participates in the generation of neuropathic pain, we used the spared nerve injury (SNI) model in rats to examine beta2 subunit expression in selectively injured (tibial and common peroneal nerves) and uninjured (sural nerve) afferents. Three days after SNI, immunohistochemistry and Western blot analysis reveal an increase in the beta2 subunit in both the cell body and peripheral axons of injured neurons. The increase persists for >4 weeks, although beta2 subunit mRNA measured by real-time reverse transcription-PCR and in situ hybridization remains unchanged. Although injured neurons show the most marked upregulation,beta2 subunit expression is also increased in neighboring non-injured neurons and a similar pattern of changes appears in the spinal nerve ligation model of neuropathic pain. That increased beta2 subunit expression in sensory neurons after nerve injury is functionally significant, as demonstrated by our finding that the development of mechanical allodynia-like behavior in the SNI model is attenuated in beta2 subunit null mutant mice. Through its role in regulating the density of mature VGSC complexes in the plasma membrane and modulating channel gating, the beta2 subunit may play a key role in the development of ectopic activity in injured and non-injured sensory afferents and, thereby, neuropathic pain

Inclusive V0V^0 Production Cross Sections from 920 GeV Fixed Target Proton-Nucleus Collisions

Inclusive differential cross sections $d\sigma_{pA}/dx_F$ and $d\sigma_{pA}/dp_t^2$ for the production of \kzeros, \lambdazero, and \antilambda particles are measured at HERA in proton-induced reactions on C, Al, Ti, and W targets. The incident beam energy is 920 GeV, corresponding to $\sqrt {s} = 41.6$ GeV in the proton-nucleon system. The ratios of differential cross sections \rklpa and \rllpa are measured to be $6.2\pm 0.5$ and $0.66\pm 0.07$, respectively, for \xf $\approx-0.06$. No significant dependence upon the target material is observed. Within errors, the slopes of the transverse momentum distributions $d\sigma_{pA}/dp_t^2$ also show no significant dependence upon the target material. The dependence of the extrapolated total cross sections $\sigma_{pA}$ on the atomic mass $A$ of the target material is discussed, and the deduced cross sections per nucleon $\sigma_{pN}$ are compared with results obtained at other energies.Comment: 17 pages, 7 figures, 5 table

A model for collisions in granular gases

We propose a model for collisions between particles of a granular material and calculate the restitution coefficients for the normal and tangential motion as functions of the impact velocity from considerations of dissipative viscoelastic collisions. Existing models of impact with dissipation as well as the classical Hertz impact theory are included in the present model as special cases. We find that the type of collision (smooth, reflecting or sticky) is determined by the impact velocity and by the surface properties of the colliding grains. We observe a rather nontrivial dependence of the tangential restitution coefficient on the impact velocity.Comment: 11 pages, 2 figure

Origin and Evolution of Saturn's Ring System

The origin and long-term evolution of Saturn's rings is still an unsolved problem in modern planetary science. In this chapter we review the current state of our knowledge on this long-standing question for the main rings (A, Cassini Division, B, C), the F Ring, and the diffuse rings (E and G). During the Voyager era, models of evolutionary processes affecting the rings on long time scales (erosion, viscous spreading, accretion, ballistic transport, etc.) had suggested that Saturn's rings are not older than 100 My. In addition, Saturn's large system of diffuse rings has been thought to be the result of material loss from one or more of Saturn's satellites. In the Cassini era, high spatial and spectral resolution data have allowed progress to be made on some of these questions. Discoveries such as the ''propellers'' in the A ring, the shape of ring-embedded moonlets, the clumps in the F Ring, and Enceladus' plume provide new constraints on evolutionary processes in Saturn's rings. At the same time, advances in numerical simulations over the last 20 years have opened the way to realistic models of the rings's fine scale structure, and progress in our understanding of the formation of the Solar System provides a better-defined historical context in which to understand ring formation. All these elements have important implications for the origin and long-term evolution of Saturn's rings. They strengthen the idea that Saturn's rings are very dynamical and rapidly evolving, while new arguments suggest that the rings could be older than previously believed, provided that they are regularly renewed. Key evolutionary processes, timescales and possible scenarios for the rings's origin are reviewed in the light of tComment: Chapter 17 of the book ''Saturn After Cassini-Huygens'' Saturn from Cassini-Huygens, Dougherty, M.K.; Esposito, L.W.; Krimigis, S.M. (Ed.) (2009) 537-57

Production of Radiobromide: new Nickel Selenide target and optimized separation by dry distillation

Introduction Radioisotopes of bromine are of special interest for nuclear medical applications. The positron emitting isotopes 75Br (T½ = 1.6 h; β+ = 75.5 %) and 76Br (T½ = 16.2 h; β+ = 57 %) have suitable decay properties for molecular imaging with PET, while the Auger electron emitters 77Br (T½ = 57.0 h) and 80mBr (T½ = 4.4 h) as well as the β−-emitter 82Br (T½ = 35.3 h) are useful for internal radiotherapy. 77Br is additionally suited for SPECT. The isotopes 75Br, 76Br and 77Br are usually produced at a cyclotron either by 3He and α-particle induced reactions on natural arsenic or by proton and deuteron induced reactions on enriched selenium isotopes [1]. As target mate-rials for the latter two reactions, earlier ele-mental selenium [2] and selenides of Cu, Ag, Mn, Mo, Cr, Ti, Pb and Sn were investigated [cf. 3–7]. Besides several wet chemical separation techniques the dry distillation of bromine from the irradiated targets was investigated, too [cf. 2, 4, 5]. However, the method needs further development. Nickel selenide was investigated as a promising target to withstand high beam currents, and the dry distillation technique for the isolation of n.c.a. radiobromine from the target was optimized. Material and Methods Crystalline Nickel-(II) selenide (0.3–0.5 g) was melted into a 0.5 mm deep cavity of a 1 mm thick Ni plate covered with a Ni grid. NiSe has a melting point of 959 °C. For development of targeting and the chemical separation, natural target material was used. Irradiations of NiSe were usually performed with protons of 17 MeV using a slanting water cooled target holder at the cyclotron BC1710 [8]. For radiochemical studies a beam current of 3 µA and a beam time of about 1 h were appropriate. To separate the produced no-carrier-added (n.c.a.) radiobromine from the target material a dry distillation method was chosen. The apparatus was developed on the basis of a dry distillation method for iodine [cf. 9,10] and optimized to obtain the bromine as n.c.a. [*Br]bromide in a small volume of sodium hydroxide solution. Changing different components of the apparatus, the dead volume could be minimized and an almost constant argon flow as carrier medium was realized. Various capillaries of platinum, stainless steel and quartz glass with different diameters and lengths were tested to trap the radiobromine. Results and Conclusion Nickel selenide proved successful as target material for the production of radiobromine by proton irradiation with 17 MeV protons. The target was tested so far only at beam currents up to 10 µA, but further investigations are ongoing. The optimized dry distillation procedure allows trapping of 80–90 % of the produced radiobromine in a capillary. For this purpose quartz glass capillaries proved to be most suitable. After rinsing the capillary with 0.1 M NaOH solution the activity can be nearly completely obtained in less than 100 µL solution as [*Br]bromide immediately useable for radiosynthesis. So, the overall separation yield was estimated to 81 ± 5 %. The radionuclidic composition and activity of the separated radiobromide was measured by γ-ray spectrometry. Due to the use of natural selenium the determination of the isotopic purity was not meaningful, but it could be shown that the radiobromine was free from other radioisotopes co-produced in the target material and the backing. The radiochemical purity as well as the specific activity were determined by radio ionchromatography. Further experiments using NiSe produced from nickel and enriched selenium are to be per-formed. The isotopic purity of the produced respective radiobromide, the production yield at high beam currents and the reusability of the target material have to be studied